About

In the world of electronics design, the RC (Resistor-Capacitor) time constant is a fundamental parameter that dictates how fast a circuit responds to changes in voltage. Whether you are designing a simple timer, a filter, or a pulse-width modulation circuit, knowing the precise charging and discharging behavior of your capacitor is critical for signal integrity and timing accuracy.

This tool solves the differential equations for you, determining the exact voltage across a capacitor at any specific millisecond. It goes beyond simple Tau calculation by providing an interactive visualization of the exponential curve, allowing engineers and hobbyists to verify timing thresholds against standard component tolerances.

Formulas

The time constant, denoted by the Greek letter Tau (τ), is the product of resistance and capacitance:

τ = R × C

The voltage across the capacitor V_c at time t during the charging phase is calculated using the natural exponential function:

V_c(t) = V_s (1 − e^{−t / τ})

For discharging, the formula reflects the exponential decay:

V_c(t) = V₀ × e^{−t / τ}

Reference Data

Time (Units of τ)	Charge Voltage (% of V_s)	Discharge Voltage (% of V₀)	Description
0.5 τ	39.3%	60.7%	Rapid initial change
1.0 τ	63.2%	36.8%	Standard Time Constant Definition
2.0 τ	86.5%	13.5%	Significant charge accumulation
3.0 τ	95.0%	5.0%	Settling phase begins
4.0 τ	98.2%	1.8%	Near steady state
5.0 τ	99.3%	0.7%	Considered fully charged for most apps
6.9 τ	99.9%	0.1%	High precision settling

Frequently Asked Questions

At 5 Tau (5 time constants), the capacitor has reached 99.3% of its final voltage. In digital electronics and timing applications, this is practically considered 'fully charged' or 'steady state,' as the remaining 0.7% difference is usually negligible compared to component noise or tolerance.

Standard capacitors often have tolerances of ±20%, and resistors ±5% or ±1%. This means the actual time constant can vary significantly from the calculated ideal. For precision timing, it is recommended to use 1% resistors and low-tolerance capacitors (like film types), or measure the actual component values before calculation.

Mathematically, yes. The physics of RC charging scales linearly. However, in real high-voltage applications, you must also consider dielectric absorption, leakage current of the capacitor, and the voltage coefficient of the resistor, which are not accounted for in the ideal textbook formulas used here.

This calculator assumes ideal non-destructive operation. In reality, applying a reverse voltage to a polarized capacitor (like an electrolytic or tantalum cap) will destroy the dielectric layer, leading to high leakage current, overheating, and potential explosion. Always check polarity.